Action-angle variables revisited: dihedral systems, TTW-like models, black holes
Aula A1 (LNF)
Via Enrico Fermi, 40
00044 Frascati (Roma)
We demonstrate the effectivity of the use of action-angle variables in the study of novel integrable models.
At first, we construct the integrable deformations of the oscillator and Coulomb systems on N-dimensional spaces of constant curvature by replacing their angular degrees of freedom with a compact integrable (N-1)-dimensional system.As an example, we construct the spherical and pseudospherical generalization of the two-dimensional superintegrable models introduced by Tremblay, Turbiner and Winternitz (TTW) and by Post and Winternitz (PW). We demonstrate the superintegrability of these systems and give their hidden constant of motion.
Then we present a canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal
Reissner-Nordstrom and Kerr black holes and the conventional conformal mechanics.